Submitted to SIAM Journal on Control and Optimization

A robust control framework for linear, time-invariant, spatially distributed systems is outlined in this paper. We adopt an input-output approach which takes account of the spatially distributed nature of the input and output signals for such systems. The approach is a generalization of H-infinity control in the sense that the 2-norm (in both time and space) is used to quantify the size of signals. It is shown that a frequency-domain representation, in the form of a graph symbol, exists for every linear, time-invariant, spatially distributed systems under very mild assumptions. The graph symbol gives rise to left and right coprime representations if the system is also stabilizable. We investigate fundamental issues of feedback control such as feedback stability and robust stability to plant and/or controller uncertainty quantified in the gap-metric. This also includes a generalization of the Ober-Sefton gap formula to the infinite-dimensional operator case.

Key Words : spatially distributed systems, distributed-parameter systems, robust stability, gap-metric, H-infinity control